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- The below graph illustrates the relationship between the level curves and the graph of the function. The key point is that a level curve f(x, y) = c f (x, y) = c can be thought of as a horizontal slice of the graph at height z = c z = c. This slice is the intersection of the graph with the plane z = c z = c.
mathinsight.org/level_sets
The scatter plot is an X-Y diagram that shows a relationship between two variables. It is used to plot data points on a vertical and a horizontal axis. The purpose is to show how much one variable affects another.
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The below graph illustrates the relationship between the level curves and the graph of the function. The key point is that a level curve $f(x,y)=c$ can be thought of as a horizontal slice of the graph at height $z=c$.
Definition. Given a function f (x, y) f (x, y) and a number c c in the range of f f, a level curve of a function of two variables for the value c c is defined to be the set of points satisfying the equation f (x, y) =c f (x, y) = c.
A scatter plot is a visualization of the relationship between two quantitative sets of data. The scatter plot is created by turning the datasets into ordered pairs: the first coordinate contains data values from the explanatory dataset, and the second coordinate contains the corresponding data values from the response dataset.
Learning Objectives. Understand how graphs show the relationship between two or more variables and explain how a graph elucidates the nature of the relationship. Define the slope of a curve. Distinguish between a movement along a curve, a shift in a curve, and a rotation in a curve.
The pattern of dots on a scatterplot allows you to determine whether a relationship or correlation exists between two continuous variables. If a relationship exists, the scatterplot indicates its direction and whether it is a linear or curved relationship.
The relationship between level curves and the gradient vector is significant for understanding directional derivatives. The gradient vector, which points in the direction of the steepest ascent, is always perpendicular to level curves at any given point.
